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Methods of Bifurcation Theory
An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned ...
Chaos, Fractals, and Dynamics
This timely work focuses on the recent expansion of research in the field of dynamical systems theory with related studies of chaos and fractals. Integrating the work of leading mathematicians, physicists, chemists, and engineers, this research-level monograph discusses different aspects of the concepts of chaos and fractals from both experimental and theoretical points of view. Featuring the most recent advances-including findings made possible by the development of digital computers-this authoritative work provides thorough understanding of known behavior of nonlinear dynamical systems as well as considerable insight into complex aspects not yet well understood. With a broad, multidisciplinary perspective and an ample supply of literature citations, Chaos, Fractals, and Dynamics is an invaluable reference and starting point for further research for scientists in all fields utilizing dynamical systems theory, including applied mathematicians, physicists, dynamists, chemists, biomathematicians, and graduate students in these areas. Book jacket.
Normal Forms and Bifurcation of Planar Vector Fields
This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.
Hyperbolic and Viscous Conservation Laws
Here is an in-depth, up-to-date analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. This self-contained study of shock waves explains the new wave phenomena from both a physical and a mathematical standpoint. The analysis is useful for the study of various physical situations, including nonlinear elasticity, magnetohydrodynamics, multiphase flows, combustion, and classical gas dynamics shocks. The central issue throughout the book is the understanding of nonlinear wave interactions.
Infinite Dimensional Dynamical Systems
This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation a...
Differential Equations And Applications To Biology And To Industry - Proceedings Of The Claremont International Conference Dedicated To The Memory Of Starvros Busenberg (1941 - 1993)
This volume is dedicated to the memory of Professor Stavros Busenberg of Harvey Mudd College, who contributed so greatly to this field during 25 years prior to his untimely death. It contains about 60 invited papers by leading researchers in the areas of dynamical systems, mathematical studies in ecology, epidemics, and physiology, and industrial mathematics. Anyone interested in these areas will find much of value in these contributions.
Dynamical Systems
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Dynamical Issues in Combustion Theory
This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin and Foreman Williams for editing the proceedings. We also take this opportunity to thank those agenci...
